Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.

翻译：显式模型预测控制（Explicit MPC）是一种广泛使用的控制设计方法，它利用优化工具离线求解控制策略；通常，该方法被表述为半定规划（SDP）问题，或在混合系统情形下表述为混合整数半定规划问题。然而，混合整数半定规划的计算成本高昂，这促使研究者探索替代性表述形式，例如基于zonotope的模型预测控制（zonotope是一类特殊的对称多面体）。本文提出一种适用于混合系统的鲁棒显式MPC方法。更具体地，我们将现有基于zonotope的MPC方法扩展至处理乘性参数不确定性。此外，我们提出一种凸型zonotope阶数约简方法，该方法利用zonotope传播问题的迭代结构，促进zonotope生成器中的对角块结构，并降低决策变量数量。最后，我们开发了一种准无时间依赖的策略选择算法，允许系统从轨迹上的任意点启动，并避免因基于当前状态在状态空间区域隶属度的线性控制策略离散切换而产生的颤振问题。我们通过两组实验装置验证了所提方法的有效性，并在实验中改变物理参数。